WASHINGTON — When Senate Republicans entered the final stages of the health care push earlier this year, it was clearly on its last legs. At least two senators had made it known that they had no real intention of voting to repeal the Affordable Care Act, and Republican leaders were casting about for something — anything — that could get 50 votes.

The Senate voted along party lines, 52 to 48, on Wednesday to formally take up legislation that would cut taxes by as much as $1.5 trillion over 10 years, remake the corporate tax code and effect large changes to individual taxation. The routine procedural vote, so fraught during the health care debate, began an amendment process that should end in the bill’s passage by Friday.

And this time, Senate Republicans are approaching the finish line in a fundamentally different posture: confident, cooperative, even cocky.

“It’s like night and day,” said Senator John Kennedy, Republican of Louisiana. “At this point in the health care debate, people were walking out and talking about each other’s mamas and getting mad and it just wasn’t healthy, it wasn’t productive. It was like a bunch of kids in the back of a minivan.”

“This time,” he continued, “it’s very constructive and we’re trying to make a good bill better and everybody’s in good faith.”

The story of the tax legislation is in small part about lessons learned — and in large part about doing what Republicans do best.

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Senator Susan Collins, Republican of Maine, did not commit to voting for the bill but said that she was making progress on the issues that mattered most to her.Credit...Tom Brenner/The New York Times

While most Republicans had made the repeal of the Affordable Care Act a seven-year mantra, a few simply had no interest in deep cuts to Medicaid and rolling back insurance coverage that had finally given struggling constituents a measure of security. But lowering taxes is, at heart, what makes a Republican a Republican.

The senators who brought down their party’s push to repeal the Affordable Care Act do not appear eager to kill the party’s last, and only, hope for a legislative accomplishment this year. And for all their posturing, naysayers on the particular tax bill pending before the Senate have pressed for a way forward.

“It’s one of those things that’s hard to articulate, but the mood is very different,” said Senator James E. Risch, Republican of Idaho. “People really want to get to yes.”

Hurdles do remain, and the effort to satisfy some reluctant senators could anger other senators who like the bill as it is. About half a dozen Republicans, including Senators Ron Johnson of Wisconsin and Bob Corker of Tennessee, have expressed various degrees of misgivings about the tax bill, like the way it treats small businesses and its effect on an already large and growing budget deficit.

But the differences between the health and tax debates have been striking.

President Trump, who was largely disengaged from the health bill debate — he called the House’s version of repeal “mean” after celebrating its passage in the Rose Garden — has shown deeper interest in the tax overhaul. During a lunch with Senate Republicans on Tuesday, he “got pretty deep in the weeds,” Mr. Risch said.

Another big difference: Unlike the tax measure, the health bill did not go through what the Senate calls “regular order,” with a formal bill drafting in the relevant committees. That created a kind of free-for-all atmosphere in which senators who have little expertise in health care fancied themselves experts and put forth proposals that were destined to fail, said Senator Roy Blunt, Republican of Missouri.

“I think there’s a reason you have these committees of expertise,” Mr. Blunt said. “A lot of the questions that would never have been answered if you had gone through the outrageous process we went through on health care can get answered, because the people who have been working on it know the answers.”

With the health bill, no one seemed to know what the outcome would be when the Republican leadership brought the measure to a vote. In the end, Senator John McCain, Republican of Arizona, provided a dramatic thumbs-down to kill the measure on the Senate floor.

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From left, Senators Ron Johnson, Bob Corker and David Perdue during a Senate Budget Committee hearing on Capitol Hill on Tuesday.Credit...Al Drago for The New York Times

“Now people are realizing we don’t want surprises,” said Senator James Inhofe, Republican of Oklahoma. “We’re trying to survive a surprise.”

To that end, a number of senators are now in discussion with party leaders over how to tweak the bill to address their concerns. Senator Susan Collins, Republican of Maine, who helped doom the health care measure, received assurances from Mr. Trump that he would back a provision to make $10,000 of local property taxes deductible, as she has requested, and that he would support legislation to stabilize health insurance markets.

“I have not made a commitment,” Ms. Collins said after Tuesday’s lunch, “but I am happy to report that I am making progress on the issues that matter most to me.”

Another senator who voted no on the health bill, Senator Lisa Murkowski of Alaska, was given good reason to vote in favor of the tax bill. Under arcane Senate rules, the tax legislation has been merged with a measure to open up the state’s Arctic National Wildlife Refuge to oil and gas drilling, a goal that dates to when Ms. Murkowski’s father, Frank, was in the Senate two decades ago. Ms. Murkowski said Wednesday that she was inclined to vote for the tax measure.

Health care is an inherently charged topic, and one that ordinary Americans can understand; tax policy is far more obtuse and clinical.

“This is something that we can deal with with much less emotion than when we’re dealing with health care,” Mr. Inhofe said. “Yes, some people worry it’s going to cost them more, but that’s all fiscal, so it’s easier to discuss.”

But perhaps the biggest difference is that, having failed to repeal the Affordable Care Act, Republicans feel intense pressure to pass the tax measure, lest they go home to their constituents empty-handed.

And for Republicans, cutting taxes is simply easier than virtually any other legislative task.

“If we fail on taxes, we’re toast,” said Senator Lindsey Graham, Republican of South Carolina. “Cutting taxes is in the Republican DNA.”